On Lp(T2)-Convergence and Móricz

• Journal title : Journal for History of Mathematics
• Volume 28, Issue 6,  2015, pp.321-332
• Publisher : The Korean Society for History of Mathematics
• DOI : 10.14477/jhm.2015.28.6.321
Title & Authors
On Lp(T2)-Convergence and Móricz
LEE, Jung Oh;

Abstract
This paper is concerned with the convergence of double trigonometric series and Fourier series. Since the beginning of the 20th century, many authors have studied on those series. Also, Ferenc $\small{M{\acute{o}}ricz}$ has studied the convergence of double trigonometric series and double Fourier series so far. We consider $\small{L^p(T^2)}$-convergence results focused on the Ferenc $\small{M{\acute{o}}ricz^{\prime}s}$ studies from the second half of the 20th century up to now. In section 2, we reintroduce some of Ferenc $\small{M{\acute{o}}ricz^{\prime}s}$ remarkable theorems. Also we investigate his several important results. In conclusion, we investigate his research trends and the simple minor genealogy from J. B. Joseph Fourier to Ferenc $\small{M{\acute{o}}ricz}$. In addition, we present the research minor lineage of his study on $\small{L^p(T^2)}$-convergence.
Keywords
double Fourier series;summability of double Fourier series;convergence of Fourier series;double trigonometric series;
Language
Korean
Cited by
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